The development of electrically small radio frequency (RF) antenna elements is important for many emerging applications, such as multi-input multi-output (MIMO) mobile communications systems and RF tagging. In the art of small antennas, a useful volumetric parameter is ka, where k is the free space wave number (k=2π/λ, where λ is free space wavelength) and a is the radius of the smallest sphere enclosing the antenna. It is well understood that, as the antenna size becomes small (particularly, when ka<0.5), the ability of the antenna to radiate effectively is substantially reduced. This fundamental limitation is commonly described in terms of the quality factor, Q, of the antenna—i.e., as antenna size is reduced, Q tends to increase.
In the absence of material or conductor loss, the Q of an antenna element is proportional to the ratio of the energy stored in the antenna to the rate at which the antenna emits radiation. Because the operating bandwidth of an antenna varies inversely with Q, it is desirable to achieve as low a Q as possible when designing a small antenna for a specific application. However, as noted, small antenna elements are typically characterized by large values of Q, due to the fact that they are not effective radiators.
A fundamental relationship between antenna size and Q has been formulated by L. J. Chu (“Physical Limitations On Omni-directional Antennas,” J. Appl. Phys, vol. 19, pp 1163-1175; 1948), which relationship is referred to herein (and in the art) as the Chu limit. That Chu limit specifies the minimum Q achievable for an antenna of size ka. Based on the teaching of Chu, the Q of an antenna (or equivalently, the Q of any self-resonant object with a single electric or magnetic dipole resonance) has been shown to obey the relationship
  Q  ≥            1                        (          ka          )                3              +                  1                  (          ka          )                    .      From this relationship it can be seen, as noted above, that decreasing the size of the resonator increases its Q and narrows its bandwidth. Of all of the problems typically encountered when designing small antennas (e.g., narrow bandwidth, impedance matching to low radiation resistance, low efficiency), the ability to design an antenna whose performance achieves low Q (high bandwidth) approaching the Chu limit is the most challenging to solve.
In the current art, very few single resonance antenna designs exist that closely approach the Chu limit. In general, however, it is well understood that performance close to the Chu limit can be achieved using antennas that make optimal use of the spherical volume encompassing the antenna. A known example of such an antenna is the spherical helix antenna, which consists of a helix structure wound into the shape of a sphere. Such a spherical helix antenna is capable of achieving Q-factors of 1.5 times the Chu limit at high efficiencies. At the same time, the complexity of the spherical helix antenna equates to high production cost, particularly at frequencies in the range of one to several GHz, where the antenna diameter is on the order of centimeters and antennas compatible with printed circuit board manufacturing techniques are preferred.
It is also known to achieve antenna Q factors that closely approach the Chu limit through the use of multiple resonance structures—e.g., the Goubau antenna, the disk loaded monopole, and the folded conical helix antenna. In principle, however, antennas based upon multiple resonances are capable of impedance matching bandwidths exceeding that achieved in single resonance antennas operating near the Chu limit. Therefore, such multiple resonance antennas do not represent optimized solutions.